11 research outputs found
Revisiting a Cutting-Plane Method for Perfect Matchings
In 2016, Chandrasekaran, V\'egh, and Vempala published a method to solve the
minimum-cost perfect matching problem on an arbitrary graph by solving a
strictly polynomial number of linear programs. However, their method requires a
strong uniqueness condition, which they imposed by using perturbations of the
form . On large graphs (roughly ), these
perturbations lead to cost values that exceed the precision of floating-point
formats used by typical linear programming solvers for numerical calculations.
We demonstrate, by a sequence of counterexamples, that perturbations are
required for the algorithm to work, motivating our formulation of a general
method that arrives at the same solution to the problem as Chandrasekaran et
al. but overcomes the limitations described above by solving multiple linear
programs without using perturbations. We then give an explicit algorithm that
exploits are method, and show that this new algorithm still runs in strongly
polynomial time.Comment: 19 page